02 Kata [ruby] - sum of even fibonacci numbers

Here is the first tentative using brute force.

class SecondKata
  def sum(limit)
    sum = 0
 
    limit.to_i.times do |i|
   fibN = fib(i)
   
   sum += fibN if fibN % 2 == 0
   
   break if fibN > limit
 end
 
 sum
  end
  
  def fib(n)
    n < 2 ? n : fib(n - 1) + fib(n - 2)
  end
end

And here is the second tentative using a little big of math magic.

class SecondKata
  def sum(limit)
    sum = 0
 n = ((Math.log(limit.to_i * (Math.sqrt 5)) * 2) + 1.618).round
 
    (6..n).each do |i|
   fibN = (4 * fib(i - 3)) + fib(i - 6)
   
   sum += fibN if fibN % 2 == 0
   
   break if fibN > limit
 end
 
 sum + 2
  end
  
  def fib(n)
    n < 2 ? n : fib(n - 1) + fib(n - 2)
  end
end